The modular ring Z4 was used to analyse the structure of the integer, N, obtained from xn − yn, x, y, n odd. The constraints on x and y associated with the probability of xn − yn = N = zn (z even) were explored. When n ∈ ̅34 (n = 3, 7, 11, 15, …) the structure of N is 4r0(4r3 + 3) that is ̅04 × ̅34. When n ∈ ̅14 (n = 5, 9, 13, 17, …) the structure of N is 4r0(4r1 + 1) that is ̅04 × ̅14. The row structures and right-end-digit patterns of the rows of (x3 − y3) and z3 were compared and shown to be incompatible, as expected.